On Mathieu-type series whose terms contain a generalized hypergeometric function and Meijer’s -function

Integral expressions are given for some families of Mathieu-type a-series and alternating a-series in the case when the series terms contain: (i) the generalized hypergeometric functions p F q and (ii) Meijer’s G -function. Using the derived integral representations, bounding inequalities are obtained for these series. The derived integral expressions and the consequent two-sided bounding inequalities generalize some known results published recently by the authors and H.M. Srivastava.